Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Course MAT-41-21-K-7

Curves in Projective Space (2V, 4.5 LP)

Course Type

SWS Type Course Form CP (Effort) Presence-Time / Self-Study
2 V Lecture 4.5 CP 28 h 107 h
(2V) 4.5 CP 28 h 107 h

Basedata

SWS 2V
CP, Effort 4.5 CP = 135 h
Position of the semester 1 Sem. irreg.
Level [7] Master (Advanced)
Language [EN] English
Lecturers
+ further Lecturers of the department Mathematics
Area of study [MAT-AGCA] Algebra, Geometry and Computer Algebra
Additional informations
Livecycle-State [NORM] Active

Contents

  • singularities of plane curves, Puiseux series,
  • projective curves in n-dimensional space, Castelnuovo's inequality,
  • classification of curves and moduli spaces,
  • Jacobian variety, Abel’s Theorem.

Literature

  • R. Miranda: Algebraic curves and Riemann surfaces,
  • F. Kirwan: Complex algebraic curves,
  • W. Fulton: Algebraic curves.

Materials

Further literature will be announced in the lecture.

Requirements for attendance (informal)

Basic knowledge of projective geometry, e.g from the courses [MAT-40-28-K-4] or [MAT-40-12-K-7]; basic knowledge of Complex Analysis, e.g. from the course [MAT-12-24-K-3].

Modules:

Requirements for attendance (formal)

None

References to Course [MAT-41-21-K-7]

Module Name Context
[MAT-41-21-M-7] Curves in Projective Space P: Obligatory 2V, 4.5 LP